BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Date iCal v2.13//NONSGML kigkonsult.se iCalcreator 2.18//
METHOD:PUBLISH
X-PUBLISHED-TTL:PT15M
BEGIN:VTIMEZONE
TZID:Asia/Tokyo
BEGIN:STANDARD
DTSTART:19510909T010000
TZOFFSETFROM:+1000
TZOFFSETTO:+0900
TZNAME:JST
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
UID:calendar.22535.field_date.0@appserver-27d44dad
DTSTAMP:20190723T133741Z
CREATED:20190218T163912Z
DESCRIPTION:.... Date\n\nMonday, February 25, 2019 - 16:00 to 17:00 ....
Description\n\nAbstract: The sphere packing problem in d dimensions asks f
or the densest packing of spheres in d-dimensional Euclidean space R^d. P
rior to 2016, the problem had only been solved in dimensions 2 and 3 (wi
th the solution in dimension 3 being Hales's famously complicated solutio
n to Kepler's conjecture), and solutions in most other dimensions were t
hought to be out of reach, except for dimensions 8 and 24 where overwhel
ming numerical and theoretical evidence supported the conjectures pointin
g at specific lattices as the optimal packings. In a breakthrough in 2016
, Maryna Viazovska published a stunning proof for the 8-dimensional case
, followed up shortly with a proof for the 24-dimensional case with seve
ral coauthors. The solutions work by using a previous reduction of the pr
oblem (due to Henry Cohn and Noam Elkies) to a problem in harmonic analys
is, and ingeniously solving that analysis problem using number-theoretic
tools - specifically, the mathematics of modular forms.\n\n \n\nIn this
talk I will give a quick survey of these developments and the beautiful
new challenges and opportunities that they open up for attacking this cla
ssical geometry problem. I will also discuss my own recent results on inf
inite series representations for the Riemann xi function and explain how
Viazovska's work, which appears not strongly related to the problem I was
studying, nonetheless provided me with useful inspiration.
DTSTART;TZID=Asia/Tokyo:20190225T160000
DTEND;TZID=Asia/Tokyo:20190225T170000
LAST-MODIFIED:20190218T163912Z
SUMMARY:[Geometry, Topology and Dynamics Seminar] Viazovska's work on the
sphere packing problem and some recent developments in number theory by D
r. Dan Romik (UC Davis)
URL;TYPE=URI:https://groups.oist.jp/manifolds/event/geometry-topology-and-d
ynamics-seminar-viazovskas-work-sphere-packing-problem-and
END:VEVENT
END:VCALENDAR